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The Inverse of a Diagonal Matrix

Suppose that we have the following $n \times n$ diagonal matrix $D = \begin{bmatrix} d_1 & 0 & \cdots &0 \\ 0 & d_2 & 0 & 0\\ \vdots & 0 & \ddots & \vdots \\ 0 & 0 & \cdots & d_n \end{bmatrix}$. This diagonal matrix is invertible if all of the entries on the main diagonal are nonzero, that is for every $i$, $d_i ≠ 0$. The inverse of matrix $D$ will also be a diagonal $n \times n$ matrix in the following form: